In this paper, we work uniform error bounds for proper orthogonal decomposition reduced order modeling (POD-ROM) of Burgers equation, considering difference quotients (DQs), introduced in [23]. In particular, we study the optimality behavior of the DQ ROM error bounds by considering $L^2(\Omega)$ and $H^1_0(\Omega)$ POD spaces. We present some meaningful numerical tests checking the optimality error behavior. Based on our numerical observations, noDQ POD-ROM errors have an optimal behavior, while DQ POD-ROM errors demonstrate an optimality/super-optimality behavior. It is conjectured that this possibly occurs because the DQ inner products allow the time dependency in the ROM spaces to take into account.

翻译：在本文中,我们根据[23] 中引入的差异商数,对汉堡方程式的正正正正正分分解减序模型(POD-ROM)进行统一差错约束。特别是,我们通过考虑$L2(\Omega)和$H1_0(Omega)美元POD空间来研究DQ ROM误差的最佳行为。我们提出了一些有意义的数字测试,以检查最佳误差行为。根据我们的数字观测,NoDQ POD-ROD误差是一种最佳行为,而DQ POD-ROD错误则表明一种最佳/超优度行为。我们推测,这可能是因为 DQ 内产允许在ROM空格中的时间依赖性加以考虑。